The paper deals with a class of abstract second order evolution inclusions involving a non-linear history-dependent operator. For this class, an existence and uniqueness result is proven. The proof is based on arguments of evolution inclusions with monotone operators and the Banach fixed point theorem. This result is applied to prove the solvability of a class of second order hemivariational inequalities with nonlinear memory term and, under an additional assumption, its unique solvability.